Convex functions as a meta-subject component of mathematical preparation of masters of pedagogical education

Abstract

The task of improving the quality of the training of mathematics teachers in the conditions of the introduction of a competence approach determines the relevance of the selection of fundamental educational objects that provide meta-subject results of students' education. One such object in the content of the mathematical preparation of masters of pedagogical education can be convex functions. The purpose of the article is to substantiate the need for in-depth study of convex functions and their applications in the professional and pedagogical preparation of a mathematics teacher and also to reveal their metasubject characteristics. Analysis of domestic and foreign scientific and scientific-methodological literature on convex functions, normative documentation for the training of mathematics teachers, theoretical modeling of the process of studying convex functions, and its experimental verification at the Vyatka State University. Monitoring of the results of experienced teaching within the framework of the developed model has shown an increase in the mathematical culture of students, the development of their critical thinking and research skills. The openness of the model of studying convex functions made it possible to differentiate the educational interests of students and build individual trajectories of learning for them. The effectiveness of the applied methodology for the forming of meta-knowledge and meta-skills of students is confirmed by methods and the results of the questionnaire. An in-depth study of convex functions should become an important component of the professional training of a mathematics teacher for a modern school. This notion is closely related to the classical and modern sections of mathematics, it constantly detects new applications and has a powerful educational potential. Representation of convex functions as a fundamental educational object allows us to speak about the scientific novelty of the study. The application of the developed model can form the basis for increasing the scientific and methodological competence of the future teacher of mathematics, which indicates the practical value of the work performed.